During steady motion of a vehicle on a level road, the power delivered to the wh

Question

During steady motion of a vehicle on a level road, the power delivered to the
wheels is used to overcome aerodynamic drag and rolling resistance (the product of the rolling
resistance coefficient and the weight of the vehicle), assuming that the friction at the bearings
of the wheels is negligible. Consider a car that has a total mass of 950 kg, a drag coefficient of
0.32, a frontal area of 1.8 m2, and a rolling resistance coefficient of 0.04. The maximum power
the engine can deliver to the wheels is 80 kW. Use the air density of 1.20 kg/m3.
a. Determine the speed at which the rolling resistance is equal to the aerodynamic drag force.
b. Determine the maximum speed of this car.

Explanation / Answer

Rolling resistance = aerodynamic force

C_roll * m*g = Cd*A*(0.5)*rho_air*u^2

0.04*950*9.81 = 0.32*1.8*0.5*1.2*u^2

u= 32.84 m/s

b.

for maximum speed,

power = rolling resistance+aerodynamic resistance

80*1000 = (0.04*950*9.81 + 0.5*1.2*u^2*1.8*0.32 )*u

u_max =55.56 m/s

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